k^2-6k-19=5

Solution for k^2-6k-19=5 equation:

k^2-6k-19=5

We move all terms to the left:

k^2-6k-19-(5)=0

We add all the numbers together, and all the variables

k^2-6k-24=0

a = 1; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·1·(-24)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*1}=\frac{6-2\sqrt{33}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*1}=\frac{6+2\sqrt{33}}{2}
$